If, x, y, z, ∈ R then value of determinant is

Explanation

For every nonzero a, (a + a⁻¹)² − (a − a⁻¹)² = 4. Thus, for a = 2^x, 3^x, 4^x, the first column minus the second column is always 4 times the third column. Hence the columns are linearly dependent, and a determinant with linearly dependent columns is zero.